In this chapter, we will begin the formal study of conduction heat transfer by introducing the fundamental rate equation, Fourier’s Law. This rate equation will then be applied to situations that are both one-dimensional and steady state. This chapter also provides an initial exposure to the formal process of deriving a differential equation by applying the First Law of Thermodynamics to a differentially small control volume. The alternative process of solving a problem using numerical techniques in which the First Law of Thermodynamics is applied to small but finite control volumes is introduced. Both of these approaches are repeated throughout the text as the problems that are considered become increasingly complex. Finally, the concept of a thermal resistance is introduced in this chapter. Thermal resistances are a primary tool for understanding heat transfer problems in order to simplify and solve them.

Chapters 7 through 9 discuss forced convection problems. In a forced convection problem the fluid is driven externally over a surface (for example by a fan or a pump). Free (or natural) convection refers to a problem where, in the absence of a temperature difference between the surface and the fluid, the fluid would be completely quiescent. However, because the density of most fluids depends at least weakly on temperature, the heating or cooling of the fluid leads to density gradients and an imbalance in the buoyancy forces (i.e., forces related to the action of gravity) that may cause fluid motion. The fluid motion in a free convection situation is fundamentally driven by density gradients that are induced in the fluid as it is heated or cooled due to the presence of a surface. The velocities induced by these density gradients are typically small and therefore the absolute magnitude of natural convection heat transfer coefficients is also small compared to forced convection values.

Chapter 7 provides a discussion of the behavior of laminar and turbulent boundary layers at a conceptual level without presenting any specific correlations that can be used to solve an external flow problem. In Section 7.3 the boundary layer equations are derived and Section 7.4 shows how, with some limitations, their solution can be expressed in terms of a limited set of nondimensional parameters: the Reynolds number, Prandtl number, and Nusselt number. These relationships are referred to as correlations.

Chapters 2 and 3 discussed the analytical and numerical solution of one-dimensional (1-D), steady-state problems. These are problems in which the temperature within the material is independent of time and varies in only one spatial dimension (e.g., x). Examples of such problems are the plane wall studied in Section 2.2, which is truly a 1-D problem, and the extended surface problems in Chapter 3 that are only approximately 1-D. The governing differential equation for these problems is an ordinary differential equation (ODE) and the mathematics required to solve the problem are straightforward.

Chapters 1 through 4 discuss steady-state problems, i.e., problems in which temperature depends on position (e.g., x and y) but does not change with time (t). Steady-state problems become progressively more difficult as the dimensionality of the problem increases from 1-D to 2-D (and even to 3-D, although this was not covered). This chapter begins the consideration of transient conduction problems, i.e., problems where temperature depends on time. This chapter specifically considers the simplest transient problem, one in which the temperature approximately depends only on time and not on position.

Chapters 7 through 10 discuss convection situations involving single-phase fluids. The thermodynamic state of the fluids in these problems is sufficiently far from their vapor dome that they do not undergo a phase change. In this chapter, two-phase convection processes are examined. Two-phase processes occur when the fluid is experiencing heat transfer near the vapor dome so that vapor and liquid are simultaneously present. If the fluid is being transformed from liquid to vapor through heat addition, then the process is referred to as boiling or evaporation. If vapor is being transformed to liquid by heat removal, then the process is referred to as condensation.

Chapter 2 considered problems that were truly one-dimensional. Energy transfer occurred only in one coordinate direction and therefore temperature varied only in that direction. In this chapter, we will examine problems that are only approximately one-dimensional, referred to generally as extended surfaces. Extended surfaces are typically thin pieces of conductive material that can be approximated as being isothermal in two dimensions and having temperature variations in only one direction. In an extended surface, energy is transferred laterally (i.e., across the thickness) but the temperature change induced by the energy transfer is sufficiently small that it can be neglected. The extended surface approximation greatly reduces the complexity of the problem and can often be applied with little loss in accuracy.

A heat exchanger is a device that is designed to transfer thermal energy from one fluid to another. Heat exchangers are everywhere in our modern society. Nearly all thermal systems employ at least one and usually several heat exchangers. The background material related to conduction and convection, presented in Chapters 2 through 11, is required to analyze and design heat exchangers. Section 12.1 reviews the applications and types of heat exchangers that are commonly encountered. The subsequent sections provide the theory and tools required to predict and understand the performance of these devices.

Heat transfer is the term used to describe the movement of thermal energy (heat) from one place to another. Heat transfer drives the world that we live in. Look around. Heat transfer is at work no matter where you currently are.

Chapters 2 through 6 consider heat transfer in a stationary medium where energy transport occurs entirely by conduction and is governed by Fourier’s Law. Thus far, convection has been considered primarily as a boundary condition for these conduction problems. Convection refers to the transfer of energy that occurs between a surface and a moving medium, most often a liquid or gas flowing through a duct or over an object. Convection processes include fluid motion and the related energy transfer. The additional terms in an energy balance related to the fluid flow often dominate the now familiar energy transport by conduction. The presence of fluid motion complicates heat transfer problems substantially and links the heat transfer problem with an underlying fluid dynamics problem. The complete solution to most convection problems therefore requires sophisticated computational fluid dynamic (CFD) tools that are beyond the scope of this book.